1. Field of the Invention
The present invention relates to a method of estimating the characteristics of an electrochemical system such as a battery, that are not directly measurable.
2. Description of the Related Prior Art
The electrochemical battery is one of the most critical components of a hybrid or electric vehicle. Sizing of the battery within the vehicle architecture is based on a simulation of the battery that precisely represents its electrical and thermal behavior at various dynamic load levels. Proper operation of the vehicle is based on a smart battery management system (BMS) whose purpose is to operate the battery with the best compromise between the various dynamic load levels. Precise and reliable knowledge of the state of charge (SoC), the state of health (SoH) and the thermal state (T) is essential for the BMS.
The state of charge (SoC) of a battery is the available capacity thereof (expressed as a percentage of its nominal capacity). Knowing the SoC allows estimation of how long the battery can continue to supply energy at a given current or how long it can absorb energy. This information conditions the operation of the entire vehicle and notably the management of the energy among its components.
Performance of a battery during its life degrades gradually due to the physical and chemical variations that occur during use, until the battery becomes unusable. The state of health (SoH), which is the available capacity after recharging (expressed in Ah), thus is a measurement of the point that has been reached in the life cycle of the battery.
The thermal state (T) of a battery conditions its performances because the chemical reactions and transport phenomena involved in the electrochemical systems are thermally activated. The initial thermal state is linked with the temperature external to the vehicle, which can be led to operate within a wide temperature range, typically between −40° C. and +40° C. The thermal state during operation evolves depending on the battery draw under charge and discharge conditions, its design and its environment.
More precise and reliable estimation of the SoC, the SoH and the thermal state T thereof consequently involves several advantages. This estimation helps prevent the vehicle supervisor from functioning too conservatively regarding use of the energy potential of the battery or inversely. It also allows avoiding safety oversizing of the battery and therefore saving on-board weight and, consequently, consumed fuel and it also allows reduction of the total cost of the vehicle. A correct estimator thus guarantees efficient and reliable use of the battery capacity over the entire operating range of the vehicle.
The SoC estimation method referred to as “Coulomb counting” or “book keeping” is known, but it leads to estimation errors by disregarding phenomena such as self-discharge.
No-load voltage measurement as a SoC indicator is also known. Use of other indicators for the estimation of internal resistance is disclosed in U.S. Pat. No. 6,191,590 and EP Patent 1,835,297.
The latter two methods are characterized by the fact that the SoC is first associated with one or more measurable or easily assessable quantities, through static mappings or analytical functional dependencies. However, these dependencies are in fact much more complicated than what is taken into account in the BMS, which often leads to SoC estimation errors.
A potentially more promising method is based on the measurement, by impedance spectroscopy (EIS), of a physical quantity parametrized by the SoC. For example, U.S. Published Application 2007/0090843 suggests determining the frequency f± associated by EIS with the capacitive/inductive transition. A correlation between frequency f± and the SoC is presented for a lead battery, for Ni—Cd batteries and Ni-MH batteries.
A similar approach is based on modelling the EIS spectra by equivalent electric circuits whose components are parametrized by the SoC, as described in U.S. Pat. No. 6,778,913 filed by the Cadex Electronics Company to provide an automotive battery tester Spectro CA-12 based on the multi-frequency electrochemical impedance spectroscopy for the acid-lead pair. The EIS spectra are approximated by equivalent electric circuits and the evolution of the components is parametrized by the SoC. Similarly, U.S. Pat. No. 6,037,777, filed by K. S. Champlin, determines the state of charge and other battery properties by measuring the real and imaginary parts of the complex impedance or admittance for lead batteries or other systems.
An alternative approach is based on mathematical battery models using estimation techniques known in other fields. In general terms, there are two main categories of models of the electrical and thermal behavior of batteries allowing simulation electrochemical system which are on the one hand, the electrochemical models inspired by Newman's work, based on the knowledge of the chemical reactions and the physical-chemical phenomena that take place on a microscopic scale in the battery cell and on the other hand, the models with equivalent electric circuits, using electric elements such as resistors, capacities, inductances, arranged in series and/or in parallel, to best represent the behavior dynamics of a battery.
Modelling the behavior of batteries by electric analogy is the commonest procedure because such models are intuitive ones, with concentrated parameters (that is, depending only on time), which procedure does not have time consuming calculations. The electric elements, most often identified by a physical measurement, are parametrized by the SoC, the state of health SoH, the temperature T and the value of the current (given in form of mappings).
U.S. Published Patent Application 2007/0,035,307 notably describes a method of estimating the state variables and the parameters of a battery from operating data (voltage U, current I, T), using a mathematical battery model. The mathematical model comprises a plurality of mathematical submodels which provide faster response. The submodels are models of equivalent electric circuit type, referred to as RC models, associated with restricted frequency ranges.
The use of RC models is also described in EP Patent 0,880,710 (Philips), including the description of the electrochemical and physical phenomena at the electrodes and in the electrolyte serving as a support for the development of the RC model. The temperature of the battery is simulated by the model in order to gain precision in relation to an external measurement.
In the models of RC type, the SoC is always introduced only to parametrize other variables. The SoC itself is never mentioned as an electrochemical variable. The prediction accuracy of the models by electric analogy depends on the experimentally established mappings, with a limited number of tests. These models therefore often have difficulty accounting precisely for the battery dynamics under nominal and extreme operating conditions, under high or zero current involving relaxation phenomena in the battery spread over several hours before return to thermodynamic equilibrium is voided.
In the electrochemical models, the equations of the kinetics of the main electrochemical reactions, complemented by the mass and charge balances on the scale of an element, constitute a system of algebraic-differential equations whose solution gives, at any time, the concentration of the active species. The SoC is defined from the concentrations of the active species at the electrodes.
Another SoC estimation method known in the literature (Gu, White, etc.) is based on the mathematical description of the reactions of an electrochemical system. The SoC is calculated from state variables of the system. This description rests on material, charge, energy balances and on semi-empirical correlations. The French patent application Ser. No. 08/01,709, filed on 28 Mar. 2008, entitled “METHOD OF ESTIMATING THE NON-MEASURABLE CHARACTERISTICS OF AN ELECTROCHEMICAL SYSTEM,” corresponding to U.S. Ser. No. 12/919,721, is based on the mathematical description of the reactions of an electrochemical system allowing obtaining a reference model, and then to derive therefrom a reduced model of the behavior of the battery from the reference model. However, the charge redistribution and relaxation phenomena in the battery, after more than twenty (20) seconds, are always disregarded.
Surprisingly enough, it has been found that a method comprising a mathematical description of the reactions of an electrochemical system directly in form of a 0D model (that is based on a “zero-dimensional” approximation, as detailed below) accounts for the dynamic behavior of a battery under high current and under zero current, with increased precision, synchronously with the operation of the battery, and it also allows more fine estimation of the non-measurable internal characteristics of an electrochemical system.